Question

Unknown to a medical researcher, 10 out of 15 patients have a heart problem that will result in death if they receive the test drug. 5 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that less than 4 patients will die? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Sample size = n = 5

Probability = p = 10/15 = 0.6667

X: Number of patients

X follows Binomial distribution.

PMF of Binomial distribution is

We have to find P(X < 4)

P(X < 4) = 1 - P(X 4)

P(X 4) = P(X = 4) + P(X = 5)

P(X 4) = P(X = 4) + P(X = 5) = 0.3292 + 0.1317 = 0.4609

P(X < 4) = 1 - P(X 4) = 1 - 0.4609 = 0.5391

The probability that less than 4 patients will die is 0.5391